Algebra Examples

$- 10 x - (8 x - 4 y + 2 z) + (5 x - 4 y - 2 z) - (10 x - 3 y - 4 z)$

Step 1

Remove parentheses.

$- 10 x - (8 x - 4 y + 2 z) + 5 x - 4 y - 2 z - (10 x - 3 y - 4 z)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 10 x - (8 x) - (- 4 y) - (2 z) + 5 x - 4 y - 2 z - (10 x - 3 y - 4 z)$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $8$ by $- 1$ .

$- 10 x - 8 x - (- 4 y) - (2 z) + 5 x - 4 y - 2 z - (10 x - 3 y - 4 z)$

Step 2.2.2

Multiply $- 4$ by $- 1$ .

$- 10 x - 8 x + 4 y - (2 z) + 5 x - 4 y - 2 z - (10 x - 3 y - 4 z)$

Step 2.2.3

Multiply $2$ by $- 1$ .

$- 10 x - 8 x + 4 y - 2 z + 5 x - 4 y - 2 z - (10 x - 3 y - 4 z)$

Step 2.3

Apply the distributive property.

$- 10 x - 8 x + 4 y - 2 z + 5 x - 4 y - 2 z - (10 x) - (- 3 y) - (- 4 z)$

Step 2.4

Simplify.

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Step 2.4.1

Multiply $10$ by $- 1$ .

$- 10 x - 8 x + 4 y - 2 z + 5 x - 4 y - 2 z - 10 x - (- 3 y) - (- 4 z)$

Step 2.4.2

Multiply $- 3$ by $- 1$ .

$- 10 x - 8 x + 4 y - 2 z + 5 x - 4 y - 2 z - 10 x + 3 y - (- 4 z)$

Step 2.4.3

Multiply $- 4$ by $- 1$ .

$- 10 x - 8 x + 4 y - 2 z + 5 x - 4 y - 2 z - 10 x + 3 y + 4 z$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $- 10 x - 8 x + 4 y - 2 z + 5 x - 4 y - 2 z - 10 x + 3 y + 4 z$ .

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Step 3.1.1

Subtract $4 y$ from $4 y$ .

$- 10 x - 8 x - 2 z + 5 x + 0 - 2 z - 10 x + 3 y + 4 z$

Step 3.1.2

Add $- 10 x - 8 x - 2 z + 5 x$ and $0$ .

$- 10 x - 8 x - 2 z + 5 x - 2 z - 10 x + 3 y + 4 z$

Step 3.2

Subtract $8 x$ from $- 10 x$ .

$- 18 x - 2 z + 5 x - 2 z - 10 x + 3 y + 4 z$

Step 3.3

Add $- 18 x$ and $5 x$ .

$- 13 x - 2 z - 2 z - 10 x + 3 y + 4 z$

Step 3.4

Subtract $10 x$ from $- 13 x$ .

$- 23 x - 2 z - 2 z + 3 y + 4 z$

Step 3.5

Subtract $2 z$ from $- 2 z$ .

$- 23 x - 4 z + 3 y + 4 z$

Step 3.6

Combine the opposite terms in $- 23 x - 4 z + 3 y + 4 z$ .

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Step 3.6.1

Add $- 4 z$ and $4 z$ .

$- 23 x + 3 y + 0$

Step 3.6.2

Add $- 23 x + 3 y$ and $0$ .

$- 23 x + 3 y$